The inverse conjunction fallacy

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.]

The Seiberg-Witten Map on the Fuzzy Sphere

We construct covariant coordinate transformations on the fuzzy sphere and utilize these to construct a covariant map from a gauge theory on the fuzzy sphere to a gauge theory on the ordinary sphere. We show that this construction coincides with the Seiberg-Witten map on the Moyal plane in the appropriate limit. The analysis takes place in the algebra and is independent of any star-product representation.Comment: 30 pages, references adde

Generalizing Optical Geometry

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson, Class. Quantum Grav. 23 (2006) 1) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity.Comment: 19 pages, 1 figure. A more general analysis is presented than in the former version. See also the companion papers arXiv:0708.2493, arXiv:0708.2533 and arXiv:0708.253

Absorption and Emission Characteristics of Diffuse Spherical Enclosures

The thermal radiation characteristics of spherical cavities are of practical interest in connection with the absorption of radiant energy for both space-vehicle and terrestrial applications. Also, spherical cavities are of potential use as sources of black-body energy. The purpose of this brief paper is to determine both the absorption and emission characteristics of spherical cavities which are diffuse reflectors and emitters

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

Effects of surface forces and phonon dissipation in a three-terminal nano relay

We have performed a theoretical analysis of the operational characteristics of a carbon-nanotube-based three-terminal nanorelay. We show that short range and van der Waals forces have a significant impact on the characteristics of the relay and introduce design constraints. We also investigate the effects of dissipation due to phonon excitation in the drain contact, which changes the switching time scales of the system, decreasing the longest time scale by two orders of magnitude. We show that the nanorelay can be used as a memory element and investigate the dynamics and properties of such a device

Degree growth of meromorphic surface maps

We study the degree growth of iterates of meromorphic selfmaps of compact Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show that the degrees grow similarly to those of mappings that are algebraically stable on some birational model.Comment: 17 pages, final version, to appear in Duke Math Journa

Asymptotic wave-splitting in anisotropic linear acoustics

Linear acoustic wave-splitting is an often used tool in describing sound-wave propagation through earth's subsurface. Earth's subsurface is in general anisotropic due to the presence of water-filled porous rocks. Due to the complexity and the implicitness of the wave-splitting solutions in anisotropic media, wave-splitting in seismic experiments is often modeled as isotropic. With the present paper, we have derived a simple wave-splitting procedure for an instantaneously reacting anisotropic media that includes spatial variation in depth, yielding both a traditional (approximate) and a `true amplitude' wave-field decomposition. One of the main advantages of the method presented here is that it gives an explicit asymptotic representation of the linear acoustic-admittance operator to all orders of smoothness for the smooth, positive definite anisotropic material parameters considered here. Once the admittance operator is known we obtain an explicit asymptotic wave-splitting solution.Comment: 20 page